Help needed desperately!

Suppose we place a chamber 10.0cm long with flat parallel windows in one arm of a Michelson Interferometer that is being illuminated by 600-nm light. If the refractive index of air is 1.00029 and all the air is pumped out of the cell, how many fringe-pairs will shift by in the process?

for this problem, i can't visualize the design of the interferometer at all. All i'm thinking is that m=finge-pairs?, so m=2xn/λo = 333430???

Any help would be good...at least let me know if i'm going to the right direction or not.

Your in the right direction, you calculated the number of wavelengths found when traversing the length of the chamber, twice. Now just subtract the number of wavelengths you would encounter by evacuating the chamber. (Index = 1) This will give you the change in wavelengths which happens to be the number of fringe changes. Hope this helps.